Chapter 13

Parameters and statistics

1. Compare and contrast a parameter of a population and a statistic of a sample.
2. Recognize the notation of using Greek letters for parameters and Roman letters for statistics.
3. Given the description of a statistical problem, identify whether a numerical characteristic is a population parameter or a sample statistic.

Statistical estimation and sampling distributions

1. Define sampling distribution, and relate it to prior concepts in the course such as random variables, probability distributions, and density curves.
2. Explain why we can model the statistic of a sample as a random variable when the sample was a simple random sample from a population.

The sampling distribution of \(\bar{X}\)

1. State the mean \(\mu_{\bar{X}}\) of the sample mean \(\bar{X}\) of a simple random sample.
2. State the standard deviation \(\sigma_{\bar{X}}\) of the sample mean \(\bar{X}\) of a simple random sample.
3. Explain, using the mean and standard deviation of the sample mean, why averaging values from a simple random sample is a good idea.
4. Relate the sampling distribution of the sample mean to the concepts of accuracy and precision.
5. Given a population mean and standard deviation, compute the mean and standard deviation of the sample mean from a simple random sample of the population.

The central limit theorem

1. State under what conditions the sampling distribution of the sample mean is exactly Normal.
2. State under what conditions the sampling distribution of the sample mean is approximately Normal.
3. Answer probability queries about the sample mean from a simple random sample given the relevant characteristics of the sample and the population.